A total of 2 reviews of this product on Reddit.
Wallpaper can be removed although you will need to paint afterward. How to is everywhere on the internet. If it is older paper that does not peel easily, the trick is to wet it and then walk away for a good 15 minutes. (Or even 30 with towels on the floor for the dripping. You may even need to re-wet because it got absorbed and began to dry. After that good soak the scraping should be much easier.
I have not looked a the costs of Murphy beds lately. Could work.
Or I got these. It would be a full size bed, but a whole 18” off the ground. You could store everything else in the room under that sucker! Buy a basic headboard from A also for another $100-ish. I would put the bed on the opposite wall (so it is immediately to the right when you walk in with a narrow bedside table).
Now the back corner with the brick opens up. A couple of possibilities: Flip the desk to that wall, so it does not look squished in and then put a small accent chair where the desk is. (You could then get a teeny bit larger desk for a workspace. The room will feel more spacious with the back opened up. You should still have the room for the kennel/pen when needed.
I would say definitely buy a frame. I got mine from Amazon, where you can find tons of inexpensive metal frames that are easy to set up. The box spring is really only necessary if you need extra padding between your mattress and the bed frame, but AFAIK it doesn’t make a difference in protecting yourself from bedbugs. I hope you don’t have to throw out any more of your belongings. 🙁